Resources (Updated 2/14)
Office Hours
Mon, Tue Period 6, Room 719D
Wed, Thu Period 7, Room 719D
You may drop by Room 719D whenever I am free (see Dr. Freeman's Daily Schedule posted above), and I will help you if I am available. If you would like to guarantee my availability, or require more than 10 minutes, I would invite you to schedule an appointment, either by email or in person.
Announcements (Updated 5/26)
Exam 3 Part 2 (Take-Home) (link removed)
Exam 3 will cover the material in Chapters 4 and 5 in the textbook.
Exam 3 Part 1 (55%) will be in class Tuesday 5/23. No resources will be permitted for Part 1.
Exam 3 Part 2 (45%) will be "take-home". It will be posted on Tuesday 5/23 by 4 PM and will be due on Wednesday 5/24 by by 9 AM. For Part 2, you will be permitted to use the textbook and any notes in your own handwriting. All other resources, including the use of humans and/or other internet resources will be prohibited.
Please turn in Homework 22 to count as Quiz 9. Due in class (by 11:45 AM) on Friday 5/12. Please note: (1) Presentation Counts! You will be held to an even higher standard of neatness and clarity for take-home assessments. (2) If you are absent on Friday 5/12, you must submit your work electronically (please use PDF format) before the same deadline; there will be no late work accepted or make-up assignments given. (3) Although discussing the problems with others is permitted, your written work should be your own, and is subject to the BHSEC Queens Academic Honesty Policy.
Please turn in (1) Problem 34 and (2) either Problem 22 or Problem 23 in Homework 20 to count as Quiz 8. Due in class (by 11:45 AM) on Friday 5/5. Please note: (1) Presentation Counts! You will be held to an even higher standard of neatness and clarity for take-home assessments. (2) If you are absent on Friday 5/5, you must submit your work electronically (please use PDF format) before the same deadline; there will be no late work accepted or make-up assignments given. (3) Although discussing the problems with others is permitted, your written work should be your own, and is subject to the BHSEC Queens Academic Honesty Policy.
The answers to the practice problem given in class today is:
a) C(5,0) C(5,4) + C(5,1) C(5,3) = (1)(5) + (5)(10) = 55
b) 100% (There will always be zero Purple members. Zero is at most 1 ("at most" means "less than or equal to").
Exam 2 will be on Tuesday 4/25. The format will be similar to Exam 1. The coverage includes:
Chapters 2 & 3, including any related material discussed in class
Properties of GDF's as they pertain to YNVS's
Permutations, Combinations, Factorials, etc. - Basic Counting Problems
Conditional Statements: Inverse, Converse, & Contrapositive, especially as they pertain to the results of Chapter 2
2x2 Strictly Ordinal Games, Dominant Strategies, Nash Equilibria (as agreed in class Monday 4/24)
Please turn in Problem 20 on Page 107 to count as Quiz 7. Due in class (by 11:45 AM) on Tuesday 4/18. Please note: (1) Presentation Counts! You will be held to an even higher standard of neatness and clarity for take-home assessments. (2) If you are absent on Tuesday 4/18, you must submit your work electronically (please use PDF format) before the same deadline; there will be no late work accepted or make-up assignments given. (3) Although discussing the problems with others is permitted, your written work should be your own, and is subject to the BHSEC Queens Academic Honesty Policy.
Please turn in Problems 24 and 27 on Pages 69/70 (from HW 15) to count as Quiz 6. Due in class (by 11:45 AM) on Monday 4/3. Please note: (1) Presentation Counts! You will be held to an even higher standard of neatness and clarity for take-home assessments. (2) If you are absent on Monday 4/3, you must submit your work electronically before the same deadline; there will be no late work accepted or make-up assignments given. (3) Although discussing the problems with others is permitted, your written work should be your own, and is subject to the BHSEC Queens Academic Honesty Policy.
Exam 1 has been moved to Friday 3/17.
Quiz 4 on Friday 3/10 will cover Logic.
Please turn in Problem 28 on Page 43 (from HW 5) to count as Quiz 3. Due in class (by 11:45 AM) on Friday 3/3. Please note: (1) Presentation Counts! You will be held to an even higher standard of neatness and clarity for take-home assessments. (2) If you are absent on Friday 3/3, you must submit your work electronically before the same deadline; there will be no late work accepted or make-up assignments given. (3) Your work should be your own, and is subject to the BHSEC Queens Academic Honesty Policy.
The first Quiz is postponed until Monday 2/13 due to the snow day.
Welcome to Math & Politics.
Homework (Updated 6/2)
(You are responsible for all Homework posted and/or updated before 5:00 PM the school day before the due date. Due dates are subject to change, so please check them carefully.)
HW Design Your Own Final Exam
Make up one or two good multiple choice Final Exam questions (5 choices) . Submit via email by Mon 6/5. If I like your question, I may it include it on the Final Exam. Questions should be not too hard, not too easy, and assess understanding of some important point from the course.
Due Mon 6/5 by 4PM
HW 30 (Fair Division, M=3)
Page 332 Problems 3 & 6
Due Mon 6/5
HW 29 (Adjusted Winner Manipulation)
Read Section 11.3 in the Textbook and do Page 332 Problem 2
Due Thu 6/1
HW 28 (O'Neill's Theorem)
Page 349 Problem 3
Due Tue 5/30
HW 27 (Dollar Auction)
Page 200 Problems 1, 3, and 25
Due Mon 5/22
HW 26 (Adjusted Winner)
Page 177 Problems 13, 14, 15
Due Fri 5/19
HW 25 (Cakes & Knives)
Do this problem (Updated 5/16).
Due Fri 5/19
HW 24 (Fair Division 2)
Page 175 Problems 6, 7, 8, 9
Also determine whether or not you agree with Jonah's assertion that any allocation of homogeneous assets (whether discrete or infinitely divisible) is Efficient.
Due Mon 5/15
HW 23 (Fair Division 1)
For the last example discussed in class on Thu 5/11, modify the numbers in the 3 x 3 table to prove (by example) that a Proportional allocation is not necessarily Envy-Free.
Due Fri 5/12
HW 22 (Apportionment 2)
Please complete a semi-formal write-up of the problem distributed in class on Tue 5/9 and be prepared to hand it in.
Due Fri 5/12
HW 21 (Apportionment 1)
For the example discussed in class (P1=6, P2=6, P3=2, N=10 and N=11), calculate the apportionment using Jefferson's Method. Does it work? What goes wrong?
Due Mon 5/8
HW 20 (More 2 x 2 Games, Theory of Moves)
Page 151 Problems 20, (22 or 23), 25, 34, 35
Due Tue 5/2
HW 19 (2 x 2 Strictly Ordinal Game)
Consider the following game:
Player 1 preference list (starting with most preferred outcome): CN, CC, NN, NC
Player 2 preference list (starting with most preferred outcome): NC, NN, CN, CC
a) Put the game in standard matrix form
b) For both players, determine whether or not there is a dominant strategy
c) For each outcome, determine whether or not it is a Nash Equilibrium
Due Mon 4/24
HW 18 (The Chair's Paradox)
With the sincere preferences defined as in class (and in the textbook):
1) Show that neither voter B nor voter C has a weakly dominant strategy (making no assumptions about voter A's strategy)
2) Assuming voter A votes rationally, does voter B have a weakly dominant strategy (making no assumptions about voter C's strategy)?
Due Thu 4/20
HW 17 (Political Power 1)
Page 106 Problems 15, 17, 18, 19
Due Fri 4/6
HW 16 (Counting)
Page 105 Problems 3, 4, 5, 6, 7
Due Tue 4/4
HW 15 (Trade Robustness )
Page 65 Problems 9a: List all "types" of minimal winning coalitions. (I found six types - see if you agree.)
Page 65 Problems 22, 23, 24, 27, 28
Due Mon 4/3 (but please complete as much as you can for Thu 3/30)
HW 14 (Swap Robustness Continued)
Page 65 Problems 9b: Count only the minimal winning coalitions. (Due not count the total wining coalitions and do not count either for Problem 9a. Those calculations are tedious.)
Page 65 Problems 18, 19
Due Tue 3/28
HW 13 (Swap Robustness)
Page 65 Problems 7, 8, 9, 14
Due Mon 3/27
HW 12 (Weighted Voting Systems)
1) Read Chapter 2 Sections 2.1-2.3
2) Page 65 Problems 4, 5
Due Tue 3/21
HW 11 (Logic Proofs)
1) Logic Proof Handout Problems 11-23 odd
2) Geometry Short Story Read the story, and attempt to resolve the paradox.
Due Mon 3/13
HW 10 (Conditionals & Biconditionals)
Do these problems.
Due Tue 3/7
HW 9 (Negation and DeMorgan's Laws)
Do these problems.
Due Mon 3/6
Take-Home Quiz
See Announcements above.
Due Fri 3/3
HW 8 (GDF Property Review)
1) Consider the GDF defined by "Every candidate that gets at least one first place vote is a winner". For definiteness, assume M = 5 and N= 100. Consider the properties: Resolution, Anonymity, Neutrality, AAW, CWC, IIA, Monotonicity, Pareto Efficiency, Manipulability, and Group Manipulability. State whether or not the GDF has each of these properties, and give a brief explanation.
2) Design your own version of Quiz 2. In other words, (without referring to the profiles used on the actual Quiz) come up with profiles (or pairs of profiles) and corresponding winners for which it can be concluded that one and only one of the properties listed above does NOT hold.
Due Thu 3/2
HW 7 (Manipulation)
Prove that Borda Count is not manipulable when M = 3
Due Tue 2/28
HW 6 (Manipulation)
Problems 3, 4, 7, 8, 9 on the Manipulation Problem Sheet. (In Problem 7, "runoff election" means what we are calling "Top-Two Runoff".)
Due Mon 2/27
HW 5 (Misc Problems)
Page 35 Problems 28, 32, 36, 37, 39
Due Thu 2/16
HW 4b (More Criteria)
Skip "Approval Voting" for now
Page 35 Problems 21, 22, 24, 26, 30, 31
Due Mon 2/13
HW 4a (More Social Procedures)
Skip "Approval Voting" for now
Page 35 Problems 3, 4, 5, 6, 7, 12
Due Tue 2/7
HW 3 (Hare & Coombs) (Updated)
For profiles (3), (4a), and (4b) on the class handout, calculate the winner(s) using the Plurality, Top-Two Runoff, Hare, & Coombs methods.
Also take a look at To Build a Better Ballot
Due Mon 2/6
HW 2 (Group Decision Functions)
Page 35 Problems 1, 2
Due Fri 2/3
HW 1
Read Chapter 1 in the Textbook
Due Thu 2/2
Exam Results (Updated 1/30)
Note: All Test Statistics are before adding make-up points (if applicable).
Exam 1
Statistics
Solutions
Student Work
Exam 2
Statistics
Solutions
Student Work
Exam 3
Statistics
Solutions
Student Work